You can't create something like the Disney Princess franchise without creating a bit of controversy about membership. Above are some of the characters who weren't made Princesses for one reason or another. I spoke about Eilonwy and Kida. I'll cover some of the characters in the above picture with a couple of omissions and I'll also add some that aren't there in the following post.
Basically there seem to be arguments to make any female character that is featured prominently in a Disney animated feature into an official Disney Princess. I'll go through the non human ones, with one exception first.
This is in order Faline (Bambi. I picked a shot of her as a fawn first meeting a young Bambi, because it's so cute), Lady (Lady and the Tramp), Perdita (101 Dalmatians), Duchess (The Aristocats) and Nala (The Lion King). I could have also included Miss Bianca from The Rescuers and The Rescuers Down Under, but I've never really seen anything that suggests she be made a Princess.
Disney don't generally make non human characters into Princesses, and all of the above are not anthropomorphic, they're animals, who look and to a certain extent behave that way. Both Faline and Nala can make a case for being royalty as they both marry princes or kings. Despite their rather noble sounding names neither Lady or Duchess really have any claim to nobility.
Now I said there was one exception and here she is:
The cute vixen Maid Marian from Disney's version of Robin Hood. She differs from the others in that she's anthropomorphic. I've seen some excellent artwork with her as a Princess, and I'd personally like to see her added to the Pantheon. She has some claim to royalty being the ward of a king, too.
The others are in order (this is by no means a complete list, just the ones I felt deserved a bit of focus):
Alice from Alice in Wonderland. I've never really got the push to make her into a Princess. She's quite happy being a girl who had an amazing adventure. She may like to play at being a Princess, but she would never presume to be coronated (apparently that's what Disney call it when they make a character officially a Princess).
Wendy Darling from Peter Pan. Wendy is very much like Alice; a young girl who had an adventure. I think she's happy having known Peter Pan and seen Neverland and has no great desire to be a Princess. There's probably a good argument to add Tigerlily, though. She's probably got more claim to the title than Pocahontas.
For mine Esmeralda from The Hunchback of Notre Dame was the next viable human Princess. She misses on one fairly vital category. Royalty of some shape or form. I've seen it argued that she's a Princess amongst her own people, but there's no evidence in the film or the book it was based on to suggest that this is the case. However Disney do make exceptions on occasion. Mulan is one, and the non inclusion of Eilonwy and Kida despite being bonafide Princesses, are others.
Megara from Hercules could be another. In Greek mythology she is a Princess, although that's not made clear in the film she's in. If she marries Hercules she could also lay a claim of sorts. He's the son of Zeus who is King of the Gods, so that makes him Prince of the Gods and by extension Megara Princess of the Gods. It's a shame she was never added to the line up, because she's a got a distinctive look and I found her a multi layered character.
Jane Porter from Tarzan. In some respects Tarzan was King of the Jungle and that would make Jane the Queen. She sounds suitably regal too, voiced as she was in the film by Minnie Driver using her 'posh' English accent.
I really liked Lilo in Lilo and Stitch, but I think it's pushing it a bit to claim that she or her sister are Hawaiian Princesses. There's no indication of that in the film.
Vanellope von Schweetz from Wreck-It Ralph would make an awesome Princess. I've chosen to use a picture that shows her as she was for most of the film, because it just fits the character better than the over the top Princess costume she had for a bit later in it. She did immediately disqualify herself from Princesshood by declaring herself President and promising to let the position be voted on in the future. In my head canon she's too young yet to be considered as a Princess in the Pantheon, but could do so in the future when she's a bit older.